1. HPC 2.3 – Properties of Functions
Learning Targets:
-Use a graph to determine information about local maxima and minima as well as where a function is increasing, decreasing, or constant.
-Identify even and odd functions.

2. Vocabulary – Write your own definition of each word
Vocabulary – Write your own definition of each word. You can use your book/a partner to help you if you need.
Increasing –
Decreasing –
Constant –
Local Maximum –
Local Minimum –
when a function is rising
when a function is falling
when a function doesn’t rise or fall
when a function changes from increasing to decreasing
when a function changes from decreasing to increasing

3. List the interval(s) in which f is increasing:
List the interval(s) in which f is decreasing:
List the interval(s) on which f is constant:
List the number(s) at which f has a local maximum:
List the number(s) at which f has a local minimum: y
(0,2) & (7,10) 4
(2, 3)
(2,7)
(10, 0)
(4, 0)
(1, 0) x
(10,∞)
(0, -3)
x = 2 -4
x = 7

4. y 4 (2, 3) (10, 0) (4, 0) (1, 0) x (0, -3) -4 g) Find the domain:
h) Find the range:
Find the intercepts on the interval (0, 9): y
[0, ∞) 4
(2, 3)
[-3, 3]
(10, 0)
(4, 0)
(1, 0) x
(1, 0) & (4, 0)
(0, -3) -4

5. Odd vs. Even Functions ODD Functions EVEN Functions
- origin symmetry - graph contains (x, y) and (-x, -y)
y-axis symmetry
graph contains (x,y) & (-x,y)

6. Find the intercepts:
Find the domain:
Find the range:
Find the intervals on which the graph is increasing, decreasing, or constant.
Determine whether the graph is even, odd, or neither.
[-π, π]
[-1, 1]
Increasing on (-π, 0); Decreasing on (0, π)
Even because the graph has y-axis symmetry

7. HPC 2.3 – Properties of Functions (day 2)
Learning Targets:
-Find the average rate of change of a function.
-Use a graph to determine information about local maxima and minima as well as where a function is increasing, decreasing, or constant.
-Identify even and odd functions.

8. Ex 1) Determine whether the function is even, odd, or neither:

9. Ex 2) Determine whether the function is even, odd, or neither:

10. Ex 3) Graph: Consider the interval (-1, 3).
Approximate any local maxima/minima:
Determine where the function is increasing/decreasing.

11. Average Rate of Change (aka: difference quotient)
If c is in the domain of the function y = f(x), the average rate of change of f from c to x is defined as
THINK “SLOPE”

12. Ex 4) Consider the function:
Find the average rate of change from 1 to x:
Use the result from part (a) to compute the average rate of change from x = 1 to x = 2. Simplify.
Find an equation of the secant line containing (1, f(1)) and (2, f(2)).
Graph f and the secant line.

13. Ex 5) Consider the function:
Find the average rate of change from 1 to x:
Use the result from part (a) to compute the average rate of change from x = 1 to x = 2. Simplify.
Find an equation of the secant line containing (1, f(1)) and (2, f(2)).
Graph f and the secant line.

14. Ex 6) Consider the function:
Find the average rate of change from 1 to x:
Use the result from part (a) to compute the average rate of change from x = 1 to x = 2. Simplify.
Find an equation of the secant line containing (1, f(1)) and (2, f(2)).
Graph f and the secant line.